Question

Suppose a relative has promised to give you $1,000 as a gift the day you graduate. Assuming a constant interest rate of 5%, consider the present and future values of this gift depending on whether you graduate in 1 year or in 2 years.

Complete the first row of the table by determining the value of the gift in one and two years if you become engaged today.

Present Value Value in One Year Value in Two Years
Date Received (Dollars) (Dollars) (Dollars)
Today 1,000.00 ? ?
In 1 year ? 1,000.00
In 2 years ? 1,000.00

Complete the first column of the table by computing the present value of the gift if you get engaged in one year or two years. The present value of the gift is _________ if you get engaged in two years than it is if you get engaged in one year.

Answer 1

a.

Date Received Present Value Value in 1 year Value in 2 years

Today 1,000 $1,050 $1,102.50

In 1 year $952.38 $1,000

In 2 years $907.03 $1,000

Future value in 1 year if $1,000 is received today:

= 1,000 * (1 + 5%)

= $1,050

Future value in 2 years:

= 1,000 * ( 1 + 5%)²

= $‭1,102.5‬

Present value if $1,000 received in a year:

= 1,000/(1 + 5%)

= $952.38

If received in 2 years:

= 1,000 / (1 + 5%)²

= $907.03

b. The present value of the gift is smaller if you get engaged in two years than it is if you get engaged in one year.